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Archive for August, 2009

Ruin theory has always been a vital part of actuarial mathematics. At first glance, some of the theoretically derived results seem to have limited scope in practical situations. Nevertheless, calculation of and approximation to ruin probabilities have been a constant source of inspiration and technique development in actuarial mathematics.

Assume an insurance company is willing to risk a certain amount in a certain branch of insurance, i.e. if the claim surplus exceeds the level u some drastic action will have to be taken for that branch. Because in some sense this part of the business starts with the capital we can safely the initial capital. The actuary now has to make some decisions, for instance which premium should be charged and which type of reinsurance to take. Often, the premium is determined by company policies and by be to minimize the probability that the claim surplus ever exceeds the level.

To be more specific, consider the risk reserve and define the random variable. The instant gives us the man time of the portfolio, where we interpret ruin in a technical sense. Of course, we should allow the possibility that no ruin ever occurs, which means that. We should realize that is dependent on all the stochastic elements in the risk reserve process as well as on the deterministic value.

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